A novel reduced-order method using mixed nonlinear kinematics for geometrically nonlinear analysis of thin-walled structures

Abstract

Reduced-order methods based on the Koiter perturbation theory are applicable only to structural buckling problems, and high-order strain energy derivatives influence the computational efficiency of the methods. In this paper, a novel reduced-order method is proposed for the geometrically nonlinear analysis of thin-walled structures with large deflections. Mixed nonlinear kinematics are developed for the reduced-order method using co-rotational and updated von Kármán formulations. The co-rotational kinematics are applied to determine the internal force and tangent stiffness, whereas the third- and fourth-order strain energy derivatives are calculated using the updated von Kármán kinematics. Reduced-order models with one degree of freedom is constructed based on the perturbation theory, the solutions of which are nonlinear predictors of the geometrically nonlinear response. The use of mixed nonlinear kinematics significantly reduces the computational cost of constructing a reduced-order model. Nonlinear predictors are corrected using internal force-based residuals to ensure the accuracy of the geometrically nonlinear analysis. A geometrically nonlinear response with favorable smoothness is efficiently achieved using large step sizes in the path-following analysis. Various numerical examples, including the stiffened plate and wing structure, are provided to validate the accuracy and efficiency of the proposed method.